Enigma 1289: Alternate chain
4 October 2014
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From New Scientist #2447, 15th May 2004 [link]
I have constructed a cyclical chain of 3-digit numbers, where each number starts with the digit (which is never 0) that was the last digit of the previous number in the chain, and the numbers in the chain are alternately perfect squares and triangular numbers.
The chain consist of as many numbers as is possible, consistent with the requirements outlined above and the stipulation that no number may appear in it more than once.
How many numbers are there in the chain?
Note: I am still waiting for a phone line to be connected at my new house, so I only have sporadic access to the internet at the moment.